Another related body of work is that of demographic parity in fair machine learning.
The demographic parity objective [1]} for binary prediction requires that the class predicted, \(\hat{y}\) , is statistically independent of protected variables such as race or gender.
Previous work [2]} has formulated this as requiring \(I(\hat{y} ; u) = 0\)  for protected variables \(u\) , while marginalizing over the unprotected variables \(x\) . We show in the appendix (section REF ) that our approach is equivalent to the demographic parity objective for one-timestep episodes.
Therefore, our mutual-information constraint can be seen as an extension of demographic parity to the general RL setting. It is unclear whether this extension from the bandit setting makes sense as a notion of fairness: recent work has proposed different formulations of fairness for sequential decision-making, such as meritocratic fairness [3]} or path-specific fairness [4]}.
